#### Date of Submission

8-28-2009

#### Date of Award

8-28-2010

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Computer Science

#### Department

Machine Intelligence Unit (MIU-Kolkata)

#### Supervisor

Bandyopadhyay, Sanghamitra (MIU-Kolkata; ISI)

#### Abstract (Summary of the Work)

In our every day life, we make decisions consciously or unconsciously. This decision can be very simple such as selecting the color of dress or deciding the menu for lunch, or may be as difficult as those involved in designing a missile or in selecting a career. The former decision is easy to take, while the latter one might take several years due to the level of complexity involved in it. The main goal of most kinds of decision-making is to optimize one or more criteria in order to achieve the desired result. In other words, problems related to optimization galore in real life. Development of optimization algorithms has therefore been of great challenge in computer science. The problem is compounded by the fact that in many situations one may need to optimize several objectives simultaneously. These specific problems are known as multiobjective optimization problems (MOOP). In this regard, a multitude of metaheuristic single objective optimization techniques like genetic algorithms, simulated annealing, differential evolution, and their multiobjective versions have been developed.Computational pattern recognition can be viewed as a two fold task, comprising learning the invariant properties of a set of samples characterizing a class, and of deciding that a new sample is a possible member of the class by noting that it has properties common to those of the set of samples [20]. The latter classification task can be either supervised or unsupervised depending on the availability of labelled patterns. Clustering is an important unsupervised classification technique where a number of patterns, usually vectors in a multi-dimensional space, are grouped into clusters in such a way that patterns in the same cluster are similar in some sense and patterns in different clusters are dissimilar in the same sense. Cluster analysis is a difficult problem due to a variety of ways of measuring the similarity and dissimilarity concepts, which do not have any universal definition. Therefore, seeking for an appropriate cluster is experiment-oriented with the assumption that clustering algorithms capable of performing as per the demand are yet to be investigated. A good review of clustering can be found in [97].For partitioning a data set, one has to define a measure of similarity or proximity based on which cluster assignments are done. The measure of similarity is usually data dependent. It may be noted that, in general, one of the basic features of shapes and objects is symmetry which is considered to be important for enhancing their recognition [10]. As symmetry is commonly found in the natural world, it may be interesting to exploit this property while clustering a data set [24][25][26][43][169][187].The problem of clustering requires appropriate parameter selection (e.g., model and model order) and efficient search in complex and large spaces in order to attain optimal solutions. Moreover, defining a single measure of optimality is often difficult in clustering, leading to the need of defining multiple objectives that are to be simultaneously optimized. This makes the process not only computationally intensive, but also leads to a possibility of losing the exact solution.

#### Control Number

ISILib-TH364

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Saha, Sriparna Dr., "Single and Multiobjective Approaches to Clustering with Point Symmetry." (2010). *Doctoral Theses*. 378.

https://digitalcommons.isical.ac.in/doctoral-theses/378

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843732